Semiconductor modules usually contain one or more semiconductor chips, via the load paths of which high currents flow. These currents are measured by means of a shunt resistor. Shunt resistors of this type are usually mounted on a circuit carrier on which one or more of the semiconductor chips are also mounted. In this case, a sufficiently large placement area on the circuit carrier must be kept available for the shunt resistor. This increases the production costs of the module particularly when the circuit carrier is a ceramic-based circuit carrier, which is generally very expensive.